Function Operation

How to solve the operations with functions (f + g, f - g, f*g, f/g): 4 examples and their solutions.

Example 1

Example

Solution

(f + g)(x) = f(x) + g(x)

f(x) = 3x
g(x) = x2 - 1

So f(x) + g(x)
= 3x + x2 - 1.

Arrange the terms in descending order.

So
x2 + 3x - 1
is the answer.

Example 2

Example

Solution

(f - g)(x) = f(x) - g(x)

f(x) = 3x
g(x) = x2 - 1

So f(x) - g(x)
= 3x - (x2 - 1).

-(x2 - 1) = -x2 + 1

Arrange the terms in descending order.

So
-x2 + 3x + 1
is the answer.

Example 3

Example

Solution

(f⋅g)(x) = f(x)⋅g(x)

f(x) = 3x
g(x) = x2 - 1

So f(x)⋅g(x)
= 3x(x2 - 1).

So
33 - 3x
is the answer.

Example 4

Example

Solution

(f/g)(x) = f(x)/g(x)

f(x) = 3x
g(x) = x2 - 1

So f(x)/g(x)
= 3x/[x2 - 1].

So
3x/[x2 - 1]
is the answer.